Recursive constructions of irreducible polynomials over finite fields

Given the field Fq of characteristics p and an irreducible polynomial P(x)=cnxn+cn−1xn−1+⋯+c1x+c0 over Fq. We consider certain questions of the irreducibility of the composition of polynomials over finite fields for some particular cases. Furthermore, two computationally simple and explicit recursive constructions of sequences of irreducible polynomials of degree n2k and npk (k=1,2,3,…) over F2s and Fp, respectively, are given.